When a fluid flows around a cylinder, under some circumstances, transient oscillating vortices are formed behind the cylinder as illustrated in Figure 6.11. The path of these vortices is called the...

When a fluid flows around a cylinder, under some circumstances, transient oscillating vortices are formed behind the cylinder as illustrated in Figure 6.11. The path of these vortices is called the von Karm´ an vortex street. Consider the case in which a ´ fluid of density ρ and viscosity µ approaches a cylinder of diameter D and generates vortices with a frequency ω. A model is to be constructed to study this phenomenon in the laboratory. (a) What scaling law should be used to design the model? (b) In a prototype, standard air flows past a cylinder of diameter 300 mm at a velocity of 70 km/h. If the model cylinder is to have a diameter of 50 mm and the model test is to be conducted in a water tunnel using water at 20◦C, what approach velocity should be used in the model? (c) If a shedding frequency of 32 Hz is observed in the model, what shedding frequency is expected in the prototype?